McKean and Singer [1]} used a heat trace argument to show that for \(M\)  a closed manifold, Weyl's law satisfies
\( N(x) = w(x) + \frac{\omega _{n-2}}{6(2\pi )^{n-1}} \bigg ( \int _M K \bigg )\ x^{n/2 - 1} + R(x) \) 
